Any shirt that is made of polypropylene will be best for sweating.
What you want to avoid is cotton. Buy clothing that doesn't even have a percent of cotton.
Now look at different materials. Some of the cheaper dry fit type clothing (and I'm not just talking about Nike) is made of nylon. This can be abrasive on skin and actually cause irritation in some people, whereas with other's it doesn't matter.
So it all depends on what type of activity you are doing, how sensitive your skin is, how hot it is where you are, how humid it is etc.
Nike is not the only manufacturer, so they may not be the best. And not all dri-fit clothing is the same. Some are cheaper than others. If you get too cheap you will not get the quality.
The more I get into serious outdoor activities (long distance running, trail running, hiking, climbing, hunting etc.) the more I hate Nike. They make equipment for the lay person, it's relatively cheap but over all the quality doesn't stand up to serious use.
I've always been a massive fan of North Face and Goretex. For running gear I like brands designed for running like Brooks, Asics, Saucony, Mizuno etc.